Michael Nelson and Jordon Forster were on target for the visitors, who closed the gap on sixth place St Johnstone to one point with their win.
Hibs scored with their first effort at goal when Nelson rose above the home defenders to meet a Paul Cairney corner and head home on 18 minutes.
Cairney supplied the second on 56 minutes as well from another corner, and this time Forster stooped inside the six yard box to head the ball over the line.
Either side of the opening goal Melvin De Leeuw he fired his shot just wide of the upright as Hibernian only partially cleared a Graham Carey cross.
And the visitors thought they had doubled their lead when County keeper Michael Fraser could only parry a Liam Craig drive and Ryan McGivern netted the rebound only to be ruled offside.
County came close to a leveller when Carey swept in a 25-yard free-kick but the ball brushed the side netting on its way past.
After the break Carey cut inside and let fly with a right foot shot that clipped the outside of the Hibs post, with keeper Ben Williams well beaten.
Midfielder Carey was left frustrated once more with a free-kick on 73 minutes which rebounded off the crossbar.